If \(\mathcal {C}\)  has enough \(\xi \) -projectives, then for any object in \(A\in {\mathcal {C}}\) , there exists a \(\xi \) -exact complex \(@C=1.5em{\mathbf {P}[r]& A}\)  such that \(P_{i}\in \mathcal {P}(\xi )\)  for all \(i\geqslant 0\) , which is said to be a \(\xi \) -projective resolution of \(A\)  (see [1]}).
